By proving the money was lawfully acquired twice over: how the deceased came by the assets, and how they reached the investor. That means the will or grant of probate, the estate accounts and distribution record, evidence of the original source, and bank records showing the funds arriving in her own account.
The chain has to reach past the person who died
Lawful source and path of funds is the requirement that fails most often, and inherited money is a common reason. An adjudicator cannot take on trust that an estate's assets were lawfully obtained, and the person best placed to explain them is gone, so the evidence has to be assembled from records. Roseline should expect to produce the will or the grant, the executor's accounts, the schedule of assets and the distribution statement showing her share.
Behind that sits the original acquisition: property deeds and the purchase that created them, employment or business income with matching tax filings, or investment records for holdings built over decades. Where documents have been lost, secondary evidence often exists — land registry extracts, historical tax assessments, a bank's own archive, an accountant's working files — and gathering it early is far easier than answering a request for evidence later. Finally, the path must be shown: the transfer from the estate account into hers, any conversion of currency, and each subsequent movement toward the enterprise, with nothing unexplained in between.